How to make a wiggly animated curve?
Good ol' fashion hook modifier.

One way to set up a hook.

Snap 3d cursor to control point of curve in edit mode, then in object mode add an empty.  With the empty selected, shift select the curve return to edit mode,  and "Hook to selected Object" (from space search).  



Now you can animate the position of the hook to manipulate your curve.  Adding more hooks will give you more control.


Pretty crappy gif, but you get the idea.  The empty is hooked to the right control point of the default bezier curve. The empty is animated to rotate and follow a circular path.